With any normal preparation, this display would not have been unexpected; Poulter has been bubbling. At the Honda Classic three weeks ago, he looked certain to win until he hit five shots into the lakes in a startling 10-hole spell and, in his own words “threw away” a tournament that ­Padraig Harrington eventually won. Poulter was in contention last week in Tampa as well, until a third-round 75 derailed him.

“I was No 1 in proximity to the hole at Honda and 13th in proximity last week which means I’m playing good golf,” Poulter said. “This was a clean round, no bogeys and there were very few mistakes.” The highlight was the eagle at the par-five 16th, where he holed a putt from just off the green. “They always help on the scorecard,” he said.

Don’t they just. At the same hole 10 minutes earlier, world No 1 Rory McIlroy had lost the chance to hit every green in regulation for the first time in his PGA Tour career, which would have created a small piece of history.

It would have been a nice addition to McIlroy’s creaking CV as nobody in 20 years has achieved the feat at Bay Hill. But after 15 mostly flawless holes – barring a few missed putts on these awful greens – McIlroy could not resist going for the par-five 16th green in two from the rough. He came up short, the ball went splash and he laughed in frustration.

In truth, the resulting bogey was far from disastrous as he went on to post a two-under 70. And, with his shot at the career grand-slam coming up in three weeks’ time at the Masters, the improvement in his ball-striking was plainly encouraging.

The 25-year-old was disappointed with his ball-striking on his two previous starts, when he miss the cut at the Honda Classic and finished tied for ninth at the WGC Cadillac Championship. But after a few days of hard labour on the range last week with his coach, Michael Bannon, the gremlins have seemingly been eradicated.

“I hit so many greens and there were so many more quality shots than at Doral,” McIlroy said. “There’s some really promising signs and, with another three days of hopefully solid, golf I can try to get into contention and that will put me in a good place going into Augusta.

“You know, if I’d have taken more of my chances today this would have been a much lower score.”

Rory McIlroy tees off at the third

McIlroy’s profligacy on these greens was understandable. With bare patches aplenty, the putting surfaces are far softer and the grass far longer than the greenstaff would have wished and the decision has been made to blow them up – or in agronomical speak “undertake a comprehensive re-grassing project” – in the summer. Alas, for this week, the pros will have to like it and wallop it. McIlroy was not moaning, despite playing the par-fives – “the key to this course” – only in level par.

How could he on such a beautiful Florida day, with a huge gallery following? Bay Hill regulars advised that this was “a Tiger crowd” and, with the 14-time major-winner still on his indefinite leave of absence as he tries to resurrect his game, it is quite clear the role in which McIlroy has been cast.

In its Masters edition, Golf Digest, the most venerable American magazine, featured McIlroy posing as Michelangelo’s David. Alas, his slingshot was eventually to misfire on the 16th, although he restated his class with a beautiful approach to the 18th to 12 feet to conclude on a high.

Henrik Stenson, the world No 3, is in ominous form heading into the season’s first major. Having finished fourth in the past two weeks on the Florida swing, the Swede maintained this run with a four-under 68. The resurgent Harrington is on the same mark, as is Scotland’s Martin Laird.